This paper proposes a method of planar reconstruction for robotic mapping using image edge points. A major problem in image-based planar reconstruction is how to assign planes to non-textured regions. Our method samples seed points from the pixels and generates plane hypotheses using the image edge points surrounding the seed points. After pruning the plane hypotheses using visibility constraints and clustering, the optimal plane is assigned to each seed point using a graph cut algorithm. A seed point graph represents continuity constraints between seed points for the smoothness terms in the graph cut in order to correct false planes generated by occlusions. Our method can be applied to both non-textured and textured environments, and also it can reconstruct planes even from curved edges. Experiments show that our method successfully reconstructed planes in various environments.